Known winches of this kind include a drive motor for driving the two rope drums via a corresponding branching transmission. A cable rope is slung over the rope drums. In this way, a rigid mechanical drive connection is obtained. When working with the winch, it is not possible to prevent the cable rope from becoming dirty. The dirt accumulates in the peripheral grooves of the rope drum guiding the rope. In this way, a layer of dirt builds up in the peripheral grooves and especially in the peripheral grooves of the rope drum over which the dirtied rope is first guided. The layer of dirt causes the diameter and the periphery of the rope drum to increase. The rotational speed of both, rope drums is the same and the layer of dirt causes the drums to have different peripheral velocities in accordance with the degree of dirt accumulation. The tangential velocities are transmitted to the rope cable slung about the rope drums. The different velocities introduce forces which are in part considerable and can cause the transmission to become prematurely damaged.